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In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and on alternative methods to help you to gather evidence of attainment, or to identify barriers to progress, that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children’s learning, this accumulating evidence will help you to determine the level at which they are working.
To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.
In this unit the illustrated assessment focuses are:
Children respond quickly to multiplication and division calculations involving decimals. They work out calculations such as 5.6 ÷ 
= 0.7 or 3 × 0.6, drawing on their knowledge of number facts and understanding of place value. They are able to approximate, use inverses and apply tests of divisibility to check their results.
Children know the square numbers up to 12 × 12 and derive the corresponding squares of multiples of 10, for example 80 × 80 = 6400. Children investigate the factors of different numbers and establish that numbers with an odd number of factors are square numbers (for example, the factors of 9 are 1, 3 and 9).
They recognise that numbers with only two factors are prime numbers and can apply their knowledge of multiples and tests of divisibility to identify the prime numbers less than 100. They explain that 73 children can only be organised as 1 group of 73 or 73 groups of 1, whereas 44 children could be organised as 1 group of 44, 2 groups of 22, 4 groups of 11, 11 groups of 4, 22 groups of 2 or 44 groups of 1. They explore the pattern of primes on a 100-square, explaining why there will never be a prime number in the tenth column and the fourth column.
Children recognise and use sequences, patterns and relationships involving numbers and shapes to solve problems such as:
How can you use factors to calculate 35 × 14?
Investigate multiples of 25. What do you notice about the last two digits?
How could you test a number to see whether it is divisible by 8?
Investigate the differences between terms of the sequence of square numbers 1, 4, 9, 16, ...
Describe the pattern and use it to continue the sequence. Investigate the statement: 'Every square number is the sum of two triangular numbers'.
Assessment focus: Ma2, Numbers and the number system
As they work with a wider range of sequences, look for children who use negative numbers, for example, to continue a sequence back past 0. Look for evidence of children recognising and describing relationships and properties such as multiple, factor, square and prime.
Children use their knowledge of multiples to solve problems such as: My age is a multiple of 8. In a year's time, my age will be a multiple of 7. How old am I? They work systematically to find all possible solutions, tabulating the information they need to solve the problem.
Children identify parallel and perpendicular sides in 2-D shapes. They explore which quadrilaterals have pairs of parallel and/or perpendicular sides. They investigate how many pairs of parallel sides there are in regular polygons, generalising and explaining their findings and expressing them in a formula, at first in words then using symbols. They classify 2-D shapes using assorted criteria. They use their knowledge of shape properties to solve problems, for example:
How many different shapes can be made by placing two identical equilateral triangles edge to edge? What about 3, 4, 5, ... identical equilateral triangles?
Assessment focus: Ma1, Reasoning
As they investigate shapes and numbers, look for evidence of children making general statements or formulating 'rules'. Look for children who review the shapes they have sorted and can, for example, recognise that there are no triangles with more than one right angle, and can give reasons why this is so. When they work with number sequences that go up in steps of a regular size, look for children who explain a rule for working out a number in the sequence, given its position, for example, the twentieth number.
Children make and draw shapes and apply their knowledge of the properties; for example, they use art straws to create 'skeleton' shapes. They draw shapes with increasing accuracy, for example, using a set-square and ruler to draw a right-angled triangle with its two shorter sides 7.2 cm and 9.6 cm long. They find the perimeter of the triangle by measuring accurately.
Assessment focus: Ma3, Measures
As children measure shapes, look for evidence that they select appropriate measuring instruments and use them accurately. Look out for children who place the measuring instrument carefully with 0 where the measurement begins. Look for children measuring lines accurately to within 1 or 2 mm, or angles to within 2° to 5°.| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Describe the relationship between terms in this sequence: 
Explain why a square number always has an odd number of factors. |
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Tell me how to work out the area of a piece of cardboard with dimensions 30 cm by 30 cm. |
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Start from a two-digit number with at least six factors, e.g. 72. How many different multiplication and division facts can you make using what you know about 72? What facts involving decimals can you derive? |
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Can you tell me another prime number? |
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Roughly, what will the answer to this calculation be? |
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Look at this cube. How many edges are parallel to this one? How many edges are perpendicular to this one?
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Draw two straight lines from point A to divide the shaded shape into a square and two triangles.
Use your ruler and set-square to draw a 5 cm by 7 cm rectangle. |
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Convince me that in a number grid starting at 1 with nine columns, there will never be a prime number in the sixth column. |
| Activities | PDF 1MB |
| Activity 65 - Age old problems |
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Objectives for Springboard intervention unit |
Springboard unit |
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Use tests of divisibility and factors of numbers to inform and check division calculations |
Springboard 6 Unit 20 (PDF 379KB) |
| Diagnostic focus | Resource |
| Is not confident in making reasonable estimates for multiplication and division | 4 Y6 ×/÷ DfES 1162-2005 (PDF 111KB) |
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